U.S. Republican presidential candidate Rick Santorum has overwhelmingly won the caucuses in the midwestern state of Kansas, but front-runner Mitt Romney countered with solid wins in the western state of Wyoming, and the U.S. territories of Guam, the Northern Mariana Islands and the U.S. Virgin Islands.

A total of 52 delegates was at stake in the two contests — 40 in Kansas and 12 in Wyoming. Santorum picked up 33 delegates in Kansas, while Romney the remaining seven.

In sparsely populated Wyoming, Romney won seven of the 12 delegates at stake. Wyoming has the smallest population of any U.S. state, with fewer than 600,000 residents.

Romney added to his lead overnight when he won all nine delegates on the island of Guam, another nine in the Northern Mariana Islands and seven in the U.S. Virgin Islands.

Santorum's win in Kansas was a boost for his campaign as he seeks to eclipse Romney in the race to take on President Barack Obama in November.

A candidate must win 1,144 delegates to clinch the Republican presidential nomination at the national convention in Tampa, Florida, in late August. The eventual nominee will face President Obama, a Democrat, in the November election.

Romney did not campaign in Kansas, while Santorum and Texas Congressman Ron Paul both held events in the days before the caucuses. Former House of Representatives speaker Newt Gingrich also canceled a scheduled trip to Kansas to focus on the southern states of Alabama and Mississippi, which hold their primaries on Tuesday.